Puzzle's Maps Issue Resolve!.. Another litle problem

I already maped the puzzle, but I can make anything to desapear the Join lines of the puzzle. When the pieces are in final place, I can see a very thing line on the contour of each piece. How I can resolve it?

First, I would use the basic flat side outside edge. In case this still doesn't work, I would then create a plane, map it with the same movie and use an animated transparency layer map (Black to white).
The animation should only take a couple of frames to reveal the movie. Also, use the Absolute Color feature to map both the puzzle and plane. This should work if your puzzle animation is ending frontal.